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Paper IPM / P / 15131  


Abstract:  
We investigate dynamics of probe particles moving in the nearhorizon limit of extremal MyersPerry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed in []. We find the general solution of the HamiltonJacobi equations for these systems and present explicit expressions for the Liouville integrals, discuss Killing tensors and the associated constants of motion. We analyze special cases of the background nearhorizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider nearhorizon extremal vanishing horizon case which happens for MyersPerry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.
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